###
**Important Points :**

If the speed of the a boat in still water is X kmph and speed of the stream is Y kmph

- Speed of Down Stream (DS) = (X+Y) kmph
- Speed of Up Stream (US) = (X - Y ) kmph
- Speed of a boat in still water = 1/2 ( US + DS )
- Speed of Steam = 1/2 ( US - DS )

## Ques 1.

Pavan can row with a speed of 7kmph in still water . What will be his speed with stream , If the speed of stream is 3 kmph ?

**Solution :**

Speed with stream = 7+3 = 10 kmph

## Ques 2.

What time will be taken by a boat to cover a distance of 80 km along the stream , if speed of boat in still water is 6 kmph and speed of stream is 2 kmph ?

**Solution :**

Along with stream = Down Stream = 6+2 = 8 kmph

Time taken = 80/8 = 10 kmph

## Ques 3.

A boat takes 4 hours to 56 km downstream and 7 hours to row the same distance upstream . Find the boat's rate in still water and rate of current ?

**Solution :**

Speed of Downstream = 56/4 = 14 kmph

Speed of Upstream = 56/7 = 8 kmph

Speed of boat in still water = (14+8)/2 = 11 kmph

Speed of Current = (14-8)/2 = 3 kmph

## Ques 4.

A man can row 10 kmph in still water . It takes him twice as long to row up as to row down the river . Find the rate of stream ?

**Solution :**

Man speed = 10 kmph

Stream speed = X kmph

==> Time taken to travel downstream = 2 * Time taken to travel upstream

==> 10 + X = 2*(10-X)

==> X = 30/3 kmph

## Ques 5.

Ravi can row a certain distance downstream in 8 hours and can return the same distance in 12 hours . If the stream flows at the rate of 4 kmph , then find the speed of Ravi in still water ?

**Solution :**

==>. 8(x+4) = 12(x-4)

==> 8x + 32 = 12x - 48

==> X = 80/4 = 20 kmph

## Ques 6.

A man speed in still water is 15 kmph , while river is flowing with a speed of 3 kmph and time taken to cover a certain distance upstream is 3 hours more than taken to cover the same distance downstream . Find the distance .

**Solution :**

Speed of Downstream = 15+3 = 18 kmph

Speed of Upstream = 15-3 = 12 kmph

==> X/12 - X/18 = 3

==> X = 36*3

==> X = 108 km

## Ques 7.

Raghu rows in still water with a speed of 4.5 kmph to go to a certain place and to come back . Find his average speed for the whole journey , if the river is flowing with a speed of 1.5 kmph ?

**Solution :**

Raghu's speed upstream = 4.5 - 1.5 = 3 kmph

Ragu's speed downstream = 4.5+1.5 = 6 kmph

Distance = X km

Time Taken in upstream = X/3

Time Taken in downstream = X/6

Average Speed = 2X/(X/3 + X/6 ) = 4 kmph

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